Multiple choice

A velocity field is given as $\bar{V} = 2 y \hat{i} + 3x \hat{j}$ where x and y are in metres. The acceleration of a fluid particle at (x, y) = (1, 1) in the x direction is

  1. 0 m/s2

  2. 5.00 m/s2

  3. 6.00 m/s2

  4. 8.48 m/s2
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C Correct answer
Explanation

The acceleration in the x direction is given by the material derivative of u, which is ax = u * (du/dx) + v * (du/dy) + (du/dt). Given velocity components u = 2y and v = 3x, the partial derivative du/dx = 0 and du/dy = 2. Thus, ax = (2y)(0) + (3x)(2) = 6x. At (x, y) = (1, 1), ax = 6(1) = 6.00 m/s^2.

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